(D) The relationship between electric field $E$ and potential $V$ is given by $E = -\frac{dV}{dx}$.Given the potential function $V = 8x^2 + 2$.Differe

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(D) The relationship between electric field $E$ and potential $V$ is given by $E = -\frac{dV}{dx}$.Given the potential function $V = 8x^2 + 2$.Differentiating with respect to $x$,we get $\frac{dV}{dx} = \frac{d}{dx}(8x^2 + 2) = 16x$.Thus,the electric field $E_x = -16x$.At the point $(-4, 0)$,the $x$-coordinate is $x = -4$.Substituting this value into the expression for $E_x$,we get $E_x = -16(-4) = 64 \, V/m$.The magnitude of the electric field is $|E_x| = 64 \, V/m$.

Class 12 Physics Electric Potential and Capacitance Relation between Electric Field and Potential and Potential Gradient

Easy

In a certain region of space,the variation of potential with distance from the origin as we move along the $x$-axis is given by $V = 8x^2 + 2$,where $x$ is the $x$-coordinate of a point in space. The magnitude of the electric field at a point $(-4, 0)$ is .......... $V/m$.

A
$16$
B
$32$
C
$48$
D
$64$

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Electric Potential and Capacitance

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Relation between Electric Field and Potential and Potential Gradient

Potential gradient is defined as

Easy

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Distinguish between electric field and electrostatic potential.

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If the electric potential at any point $(x, y, z) \, m$ in space is given by $V = 3x^2$ volt,the electric field at the point $(1, 0, 3) \, m$ will be ............

EasyJEE MAIN 2022

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The following figure shows the electric potential $V$ as a function of position $x$ across $4$ regions on the $x$-axis. Which of the following is correct for the electric field $E$ in these regions?

DifficultMHT CET 2026

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Electric potential in a region is varying according to the relation $V = \frac{3x^2}{2} - \frac{y^2}{4}$,where $x$ and $y$ are in $m$ and $V$ is in $V$. Electric field intensity (in $N/C$) at a point $(1 \, m, 2 \, m)$ is:

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In a certain region of space,the variation of potential with distance from the origin as we move along the $x$-axis is given by $V = 8x^2 + 2$,where $x$ is the $x$-coordinate of a point in space. The magnitude of the electric field at a point $(-4, 0)$ is .......... $V/m$.

Similar Questions

Potential gradient is defined as

Distinguish between electric field and electrostatic potential.

If the electric potential at any point $(x, y, z) \, m$ in space is given by $V = 3x^2$ volt,the electric field at the point $(1, 0, 3) \, m$ will be ............

The following figure shows the electric potential $V$ as a function of position $x$ across $4$ regions on the $x$-axis. Which of the following is correct for the electric field $E$ in these regions?

Electric potential in a region is varying according to the relation $V = \frac{3x^2}{2} - \frac{y^2}{4}$,where $x$ and $y$ are in $m$ and $V$ is in $V$. Electric field intensity (in $N/C$) at a point $(1 \, m, 2 \, m)$ is:

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